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Which of the following is not true of a stationary time series?  The process generating the data has a constant mean.  The time series plot is a straight line.  The statistical properties are independent of time.  The variability is constant over time.

Question

Which of the following is not true of a stationary time series?  The process generating the data has a constant mean.  The time series plot is a straight line.  The statistical properties are independent of time.  The variability is constant over time.

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Solution

The statement that is not true of a stationary time series is: "The time series plot is a straight line."

A stationary time series does not necessarily mean that the plot of the series is a straight line. Stationarity refers to the constancy of the mean, variance, and autocorrelation over time. It does not imply that the series does not have any trend or pattern. It simply means that these patterns are consistent over time. Therefore, a stationary time series can have a variety of shapes and patterns, not just a straight line.

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